Winding is one of themost important components in power transformers.Ensuring the health state of the winding is of great importance to the stable operation of the power system.To efficiently and accurately diagnose t...Winding is one of themost important components in power transformers.Ensuring the health state of the winding is of great importance to the stable operation of the power system.To efficiently and accurately diagnose the disc space variation(DSV)fault degree of transformer winding,this paper presents a diagnostic method of winding fault based on the K-Nearest Neighbor(KNN)algorithmand the frequency response analysis(FRA)method.First,a laboratory winding model is used,and DSV faults with four different degrees are achieved by changing disc space of the discs in the winding.Then,a series of FRA tests are conducted to obtain the FRA results and set up the FRA dataset.Second,ten different numerical indices are utilized to obtain features of FRA curves of faulted winding.Third,the 10-fold cross-validation method is employed to determine the optimal k-value of KNN.In addition,to improve the accuracy of the KNN model,a comparative analysis is made between the accuracy of the KNN algorithm and k-value under four distance functions.After getting the most appropriate distance metric and kvalue,the fault classificationmodel based on theKNN and FRA is constructed and it is used to classify the degrees of DSV faults.The identification accuracy rate of the proposed model is up to 98.30%.Finally,the performance of the model is presented by comparing with the support vector machine(SVM),SVM optimized by the particle swarmoptimization(PSO-SVM)method,and randomforest(RF).The results show that the diagnosis accuracy of the proposed model is the highest and the model can be used to accurately diagnose the DSV fault degrees of the winding.展开更多
In this paper,the application of an algorithm for precipitation retrieval based on Himawari-8 (H8) satellite infrared data is studied.Based on GPM precipitation data and H8 Infrared spectrum channel brightness tempera...In this paper,the application of an algorithm for precipitation retrieval based on Himawari-8 (H8) satellite infrared data is studied.Based on GPM precipitation data and H8 Infrared spectrum channel brightness temperature data,corresponding "precipitation field dictionary" and "channel brightness temperature dictionary" are formed.The retrieval of precipitation field based on brightness temperature data is studied through the classification rule of k-nearest neighbor domain (KNN) and regularization constraint.Firstly,the corresponding "dictionary" is constructed according to the training sample database of the matched GPM precipitation data and H8 brightness temperature data.Secondly,according to the fact that precipitation characteristics in small organizations in different storm environments are often repeated,KNN is used to identify the spectral brightness temperature signal of "precipitation" and "non-precipitation" based on "the dictionary".Finally,the precipitation field retrieval is carried out in the precipitation signal "subspace" based on the regular term constraint method.In the process of retrieval,the contribution rate of brightness temperature retrieval of different channels was determined by Bayesian model averaging (BMA) model.The preliminary experimental results based on the "quantitative" evaluation indexes show that the precipitation of H8 retrieval has a good correlation with the GPM truth value,with a small error and similar structure.展开更多
In the traditional pattern classification method,it usually assumes that the object to be classified must lie in one of given(known)classes of the training data set.However,the training data set may not contain the cl...In the traditional pattern classification method,it usually assumes that the object to be classified must lie in one of given(known)classes of the training data set.However,the training data set may not contain the class of some objects in practice,and this is considered as an Open-Set Recognition(OSR)problem.In this paper,we propose a new progressive open-set recognition method with adaptive probability threshold.Both the labeled training data and the test data(objects to be classified)are put into a common data set,and the k-Nearest Neighbors(k-NNs)of each object are sought in this common set.Then,we can determine the probability of object lying in the given classes.If the majority of k-NNs of the object are from labeled training data,this object quite likely belongs to one of the given classes,and the density of the object and its neighbors is taken into account here.However,when most of k-NNs are from the unlabeled test data set,the class of object is considered very uncertain because the class of test data is unknown,and this object cannot be classified in this step.Once the objects belonging to known classes with high probability are all found,we re-calculate the probability of the other uncertain objects belonging to known classes based on the labeled training data and the objects marked with the estimated probability.Such iteration will stop when the probabilities of all the objects belonging to known classes are not changed.Then,a modified Otsu’s method is employed to adaptively seek the probability threshold for the final classification.If the probability of object belonging to known classes is smaller than this threshold,it will be assigned to the ignorant(unknown)class that is not included in training data set.The other objects will be committed to a specific class.The effectiveness of the proposed method has been validated using some experiments.展开更多
Short-term traffic flow prediction is one of the essential issues in intelligent transportation systems(ITS). A new two-stage traffic flow prediction method named AKNN-AVL method is presented, which combines an advanc...Short-term traffic flow prediction is one of the essential issues in intelligent transportation systems(ITS). A new two-stage traffic flow prediction method named AKNN-AVL method is presented, which combines an advanced k-nearest neighbor(AKNN)method and balanced binary tree(AVL) data structure to improve the prediction accuracy. The AKNN method uses pattern recognition two times in the searching process, which considers the previous sequences of traffic flow to forecast the future traffic state. Clustering method and balanced binary tree technique are introduced to build case database to reduce the searching time. To illustrate the effects of these developments, the accuracies performance of AKNN-AVL method, k-nearest neighbor(KNN) method and the auto-regressive and moving average(ARMA) method are compared. These methods are calibrated and evaluated by the real-time data from a freeway traffic detector near North 3rd Ring Road in Beijing under both normal and incident traffic conditions.The comparisons show that the AKNN-AVL method with the optimal neighbor and pattern size outperforms both KNN method and ARMA method under both normal and incident traffic conditions. In addition, the combinations of clustering method and balanced binary tree technique to the prediction method can increase the searching speed and respond rapidly to case database fluctuations.展开更多
Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the est...Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the estimators βn* and gn*forβ and g are obtained by using class K and the least square methods. It is shown that βn* is asymptotically normal and gn* achieves the convergent rate O(n-1/3).展开更多
Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear mode...Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.展开更多
The k-nearest neighbor （k-NN） method was evaluated to predict the influent flow rate and four water qualities, namely chemical oxygen demand （COD）, suspended solid （SS）, total nitrogen （T-N） and total phosphor...The k-nearest neighbor （k-NN） method was evaluated to predict the influent flow rate and four water qualities, namely chemical oxygen demand （COD）, suspended solid （SS）, total nitrogen （T-N） and total phosphorus （T-P） at a wastewater treatment plant （WWTP）. The search range and approach for determining the number of nearest neighbors （NNs） under dry and wet weather conditions were initially optimized based on the root mean square error （RMSE）. The optimum search range for considering data size was one year. The square root-based （SR） approach was superior to the distance factor-based （DF） approach in determining the appropriate number of NNs. However, the results for both approaches varied slightly depending on the water quality and the weather conditions. The influent flow rate was accurately predicted within one standard deviation of measured values. Influent water qualities were well predicted with the mean absolute percentage error （MAPE） under both wet and dry weather conditions. For the seven-day prediction, the difference in predictive accuracy was less than 5% in dry weather conditions and slightly worse in wet weather conditions. Overall, the k-NN method was verified to be useful for predicting WWTP influent characteristics.展开更多
Whale optimization algorithm(WOA)is a new population-based meta-heuristic algorithm.WOA uses shrinking encircling mechanism,spiral rise,and random learning strategies to update whale’s positions.WOA has merit in term...Whale optimization algorithm(WOA)is a new population-based meta-heuristic algorithm.WOA uses shrinking encircling mechanism,spiral rise,and random learning strategies to update whale’s positions.WOA has merit in terms of simple calculation and high computational accuracy,but its convergence speed is slow and it is easy to fall into the local optimal solution.In order to overcome the shortcomings,this paper integrates adaptive neighborhood and hybrid mutation strategies into whale optimization algorithms,designs the average distance from itself to other whales as an adaptive neighborhood radius,and chooses to learn from the optimal solution in the neighborhood instead of random learning strategies.The hybrid mutation strategy is used to enhance the ability of algorithm to jump out of the local optimal solution.A new whale optimization algorithm(HMNWOA)is proposed.The proposed algorithm inherits the global search capability of the original algorithm,enhances the exploitation ability,improves the quality of the population,and thus improves the convergence speed of the algorithm.A feature selection algorithm based on binary HMNWOA is proposed.Twelve standard datasets from UCI repository test the validity of the proposed algorithm for feature selection.The experimental results show that HMNWOA is very competitive compared to the other six popular feature selection methods in improving the classification accuracy and reducing the number of features,and ensures that HMNWOA has strong search ability in the search feature space.展开更多
Fighters and other complex engineering systems have many characteristics such as difficult modeling and testing, multiple working situations, and high cost. Aim at these points, a new kind of real-time fault predictor...Fighters and other complex engineering systems have many characteristics such as difficult modeling and testing, multiple working situations, and high cost. Aim at these points, a new kind of real-time fault predictor is designed based on an improved k-nearest neighbor method, which needs neither the math model of system nc, the training data and prior knowledge. It can study and predict while system＇s running, so that it can overcome the difficulty of data acquirement. Besides, this predictor has a fast prediction speed, and the false alarm rate and missing alarm rate can be adjusted randomly. The method is simple and universalizable. The result of simulation on fighter F-16 proved the effidency.展开更多
<正> For a wide class of nonparametric regression functions, the nearest neighbor estimator is constructed, and the uniform measure of deviation from the estimator to the regression function is studied. Under so...<正> For a wide class of nonparametric regression functions, the nearest neighbor estimator is constructed, and the uniform measure of deviation from the estimator to the regression function is studied. Under some mild conditions, it is shown that the estimators are uniformly strongly consistent for both randomly complete data and censored data.展开更多
To overcome the limitations of the traditional stage-discharge models in describing the dynamic characteristics of a river, a machine learning method of non-parametric regression, the locally weighted regression metho...To overcome the limitations of the traditional stage-discharge models in describing the dynamic characteristics of a river, a machine learning method of non-parametric regression, the locally weighted regression method was used to estimate discharge. With the purpose of improving the precision and efficiency of river discharge estimation, a novel machine learning method is proposed： the clustering-tree weighted regression method. First, the training instances are clustered. Second, the k-nearest neighbor method is used to cluster new stage samples into the best-fit cluster. Finally, the daily discharge is estimated. In the estimation process, the interference of irrelevant information can be avoided, so that the precision and efficiency of daily discharge estimation are improved. Observed data from the Luding Hydrological Station were used for testing. The simulation results demonstrate that the precision of this method is high. This provides a new effective method for discharge estimation.展开更多
In order to solve the problem of low accuracy of traditional fixed window width kernel density estimation(KDE)in radar cross section(RCS)statistical characteristics analysis,an improved Epanechnikov KDE(K-KDE)algorith...In order to solve the problem of low accuracy of traditional fixed window width kernel density estimation(KDE)in radar cross section(RCS)statistical characteristics analysis,an improved Epanechnikov KDE(K-KDE)algorithm was proposed to analyze the statistical characteristics of the engine’s backward RCS.Firstly,the K-nearest neighbor method was used to calculate the dynamic window width of the K-KDE,and the Euclidean distance of each adjacent sample was used to judge the local density of the sample,and then the window width of the kernel function was adjusted by the distance between the sample point and the nearest neighbor to complete the KDE.Secondly,based on the K-KDE and the traditional KDE algorithm,the cumulative probability density function(CPDF)of four RCS random distribution sample points subject to fixed parameters was calculated.The results showed that the root mean square error of the K-KDE was reduced by 31.2%,38.8%,38.1%and 31.9%respectively compared with the KDE.Finally,the K-KDE combined with the second generation statistical analysis models were used to analyze the statistical characteristics of the engine backward RCS.展开更多
基金supported in part by Shaanxi Natural Science Foundation Project (2023-JC-QN-0438)in part by Fundamental Research Funds for the Central Universities (2452021050).
文摘Winding is one of themost important components in power transformers.Ensuring the health state of the winding is of great importance to the stable operation of the power system.To efficiently and accurately diagnose the disc space variation(DSV)fault degree of transformer winding,this paper presents a diagnostic method of winding fault based on the K-Nearest Neighbor(KNN)algorithmand the frequency response analysis(FRA)method.First,a laboratory winding model is used,and DSV faults with four different degrees are achieved by changing disc space of the discs in the winding.Then,a series of FRA tests are conducted to obtain the FRA results and set up the FRA dataset.Second,ten different numerical indices are utilized to obtain features of FRA curves of faulted winding.Third,the 10-fold cross-validation method is employed to determine the optimal k-value of KNN.In addition,to improve the accuracy of the KNN model,a comparative analysis is made between the accuracy of the KNN algorithm and k-value under four distance functions.After getting the most appropriate distance metric and kvalue,the fault classificationmodel based on theKNN and FRA is constructed and it is used to classify the degrees of DSV faults.The identification accuracy rate of the proposed model is up to 98.30%.Finally,the performance of the model is presented by comparing with the support vector machine(SVM),SVM optimized by the particle swarmoptimization(PSO-SVM)method,and randomforest(RF).The results show that the diagnosis accuracy of the proposed model is the highest and the model can be used to accurately diagnose the DSV fault degrees of the winding.
基金Supported by National Natural Science Foundation of China(41805080)Natural Science Foundation of Anhui Province,China(1708085QD89)+1 种基金Key Research and Development Program Projects of Anhui Province,China(201904a07020099)Open Foundation Project Shenyang Institute of Atmospheric Environment,China Meteorological Administration(2016SYIAE14)
文摘In this paper,the application of an algorithm for precipitation retrieval based on Himawari-8 (H8) satellite infrared data is studied.Based on GPM precipitation data and H8 Infrared spectrum channel brightness temperature data,corresponding "precipitation field dictionary" and "channel brightness temperature dictionary" are formed.The retrieval of precipitation field based on brightness temperature data is studied through the classification rule of k-nearest neighbor domain (KNN) and regularization constraint.Firstly,the corresponding "dictionary" is constructed according to the training sample database of the matched GPM precipitation data and H8 brightness temperature data.Secondly,according to the fact that precipitation characteristics in small organizations in different storm environments are often repeated,KNN is used to identify the spectral brightness temperature signal of "precipitation" and "non-precipitation" based on "the dictionary".Finally,the precipitation field retrieval is carried out in the precipitation signal "subspace" based on the regular term constraint method.In the process of retrieval,the contribution rate of brightness temperature retrieval of different channels was determined by Bayesian model averaging (BMA) model.The preliminary experimental results based on the "quantitative" evaluation indexes show that the precipitation of H8 retrieval has a good correlation with the GPM truth value,with a small error and similar structure.
基金supported by the National Natural Science Foundation of China(Nos.U20B2067).
文摘In the traditional pattern classification method,it usually assumes that the object to be classified must lie in one of given(known)classes of the training data set.However,the training data set may not contain the class of some objects in practice,and this is considered as an Open-Set Recognition(OSR)problem.In this paper,we propose a new progressive open-set recognition method with adaptive probability threshold.Both the labeled training data and the test data(objects to be classified)are put into a common data set,and the k-Nearest Neighbors(k-NNs)of each object are sought in this common set.Then,we can determine the probability of object lying in the given classes.If the majority of k-NNs of the object are from labeled training data,this object quite likely belongs to one of the given classes,and the density of the object and its neighbors is taken into account here.However,when most of k-NNs are from the unlabeled test data set,the class of object is considered very uncertain because the class of test data is unknown,and this object cannot be classified in this step.Once the objects belonging to known classes with high probability are all found,we re-calculate the probability of the other uncertain objects belonging to known classes based on the labeled training data and the objects marked with the estimated probability.Such iteration will stop when the probabilities of all the objects belonging to known classes are not changed.Then,a modified Otsu’s method is employed to adaptively seek the probability threshold for the final classification.If the probability of object belonging to known classes is smaller than this threshold,it will be assigned to the ignorant(unknown)class that is not included in training data set.The other objects will be committed to a specific class.The effectiveness of the proposed method has been validated using some experiments.
基金Project(2012CB725403)supported by the National Basic Research Program of ChinaProjects(71210001,51338008)supported by the National Natural Science Foundation of ChinaProject supported by World Capital Cities Smooth Traffic Collaborative Innovation Center and Singapore National Research Foundation Under Its Campus for Research Excellence and Technology Enterprise(CREATE)Programme
文摘Short-term traffic flow prediction is one of the essential issues in intelligent transportation systems(ITS). A new two-stage traffic flow prediction method named AKNN-AVL method is presented, which combines an advanced k-nearest neighbor(AKNN)method and balanced binary tree(AVL) data structure to improve the prediction accuracy. The AKNN method uses pattern recognition two times in the searching process, which considers the previous sequences of traffic flow to forecast the future traffic state. Clustering method and balanced binary tree technique are introduced to build case database to reduce the searching time. To illustrate the effects of these developments, the accuracies performance of AKNN-AVL method, k-nearest neighbor(KNN) method and the auto-regressive and moving average(ARMA) method are compared. These methods are calibrated and evaluated by the real-time data from a freeway traffic detector near North 3rd Ring Road in Beijing under both normal and incident traffic conditions.The comparisons show that the AKNN-AVL method with the optimal neighbor and pattern size outperforms both KNN method and ARMA method under both normal and incident traffic conditions. In addition, the combinations of clustering method and balanced binary tree technique to the prediction method can increase the searching speed and respond rapidly to case database fluctuations.
文摘Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the estimators βn* and gn*forβ and g are obtained by using class K and the least square methods. It is shown that βn* is asymptotically normal and gn* achieves the convergent rate O(n-1/3).
文摘Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.
文摘The k-nearest neighbor （k-NN） method was evaluated to predict the influent flow rate and four water qualities, namely chemical oxygen demand （COD）, suspended solid （SS）, total nitrogen （T-N） and total phosphorus （T-P） at a wastewater treatment plant （WWTP）. The search range and approach for determining the number of nearest neighbors （NNs） under dry and wet weather conditions were initially optimized based on the root mean square error （RMSE）. The optimum search range for considering data size was one year. The square root-based （SR） approach was superior to the distance factor-based （DF） approach in determining the appropriate number of NNs. However, the results for both approaches varied slightly depending on the water quality and the weather conditions. The influent flow rate was accurately predicted within one standard deviation of measured values. Influent water qualities were well predicted with the mean absolute percentage error （MAPE） under both wet and dry weather conditions. For the seven-day prediction, the difference in predictive accuracy was less than 5% in dry weather conditions and slightly worse in wet weather conditions. Overall, the k-NN method was verified to be useful for predicting WWTP influent characteristics.
基金This work was supported by the National Natural Science Foundation of China(Grant No.2017YFC0403605 and No.11601419).
文摘Whale optimization algorithm(WOA)is a new population-based meta-heuristic algorithm.WOA uses shrinking encircling mechanism,spiral rise,and random learning strategies to update whale’s positions.WOA has merit in terms of simple calculation and high computational accuracy,but its convergence speed is slow and it is easy to fall into the local optimal solution.In order to overcome the shortcomings,this paper integrates adaptive neighborhood and hybrid mutation strategies into whale optimization algorithms,designs the average distance from itself to other whales as an adaptive neighborhood radius,and chooses to learn from the optimal solution in the neighborhood instead of random learning strategies.The hybrid mutation strategy is used to enhance the ability of algorithm to jump out of the local optimal solution.A new whale optimization algorithm(HMNWOA)is proposed.The proposed algorithm inherits the global search capability of the original algorithm,enhances the exploitation ability,improves the quality of the population,and thus improves the convergence speed of the algorithm.A feature selection algorithm based on binary HMNWOA is proposed.Twelve standard datasets from UCI repository test the validity of the proposed algorithm for feature selection.The experimental results show that HMNWOA is very competitive compared to the other six popular feature selection methods in improving the classification accuracy and reducing the number of features,and ensures that HMNWOA has strong search ability in the search feature space.
文摘Fighters and other complex engineering systems have many characteristics such as difficult modeling and testing, multiple working situations, and high cost. Aim at these points, a new kind of real-time fault predictor is designed based on an improved k-nearest neighbor method, which needs neither the math model of system nc, the training data and prior knowledge. It can study and predict while system＇s running, so that it can overcome the difficulty of data acquirement. Besides, this predictor has a fast prediction speed, and the false alarm rate and missing alarm rate can be adjusted randomly. The method is simple and universalizable. The result of simulation on fighter F-16 proved the effidency.
基金Project supported by the National Natural Science Foundation of China.
文摘<正> For a wide class of nonparametric regression functions, the nearest neighbor estimator is constructed, and the uniform measure of deviation from the estimator to the regression function is studied. Under some mild conditions, it is shown that the estimators are uniformly strongly consistent for both randomly complete data and censored data.
基金supported by the Key Fund Project of the Sichuan Provincial Department of Education (Grant No. 11ZA009)the Fund Project of Sichuan Provincial Key Laboratory of Fluid Machinery (Grant No.SBZDPY-11-5)the Key Scientific Research Project of Xihua University (Grant No. Z1120413)
文摘To overcome the limitations of the traditional stage-discharge models in describing the dynamic characteristics of a river, a machine learning method of non-parametric regression, the locally weighted regression method was used to estimate discharge. With the purpose of improving the precision and efficiency of river discharge estimation, a novel machine learning method is proposed： the clustering-tree weighted regression method. First, the training instances are clustered. Second, the k-nearest neighbor method is used to cluster new stage samples into the best-fit cluster. Finally, the daily discharge is estimated. In the estimation process, the interference of irrelevant information can be avoided, so that the precision and efficiency of daily discharge estimation are improved. Observed data from the Luding Hydrological Station were used for testing. The simulation results demonstrate that the precision of this method is high. This provides a new effective method for discharge estimation.
文摘In order to solve the problem of low accuracy of traditional fixed window width kernel density estimation(KDE)in radar cross section(RCS)statistical characteristics analysis,an improved Epanechnikov KDE(K-KDE)algorithm was proposed to analyze the statistical characteristics of the engine’s backward RCS.Firstly,the K-nearest neighbor method was used to calculate the dynamic window width of the K-KDE,and the Euclidean distance of each adjacent sample was used to judge the local density of the sample,and then the window width of the kernel function was adjusted by the distance between the sample point and the nearest neighbor to complete the KDE.Secondly,based on the K-KDE and the traditional KDE algorithm,the cumulative probability density function(CPDF)of four RCS random distribution sample points subject to fixed parameters was calculated.The results showed that the root mean square error of the K-KDE was reduced by 31.2%,38.8%,38.1%and 31.9%respectively compared with the KDE.Finally,the K-KDE combined with the second generation statistical analysis models were used to analyze the statistical characteristics of the engine backward RCS.
